Answer :

To solve for [tex]\((f - g)(2)\)[/tex], we need to understand that this expression represents the difference between the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] evaluated at [tex]\(x = 2\)[/tex].

1. Evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 2\)[/tex]:

Recall the function [tex]\(f(x) = 3x^2 + 1\)[/tex].

Plug in [tex]\(x = 2\)[/tex]:

[tex]\[ f(2) = 3(2)^2 + 1 \][/tex]

Calculate the square of 2:

[tex]\[ (2)^2 = 4 \][/tex]

Multiply by 3:

[tex]\[ 3 \times 4 = 12 \][/tex]

Add 1:

[tex]\[ 12 + 1 = 13 \][/tex]

Therefore,

[tex]\[ f(2) = 13 \][/tex]

2. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 2\)[/tex]:

Recall the function [tex]\(g(x) = 1 - x\)[/tex].

Plug in [tex]\(x = 2\)[/tex]:

[tex]\[ g(2) = 1 - 2 \][/tex]

Subtract 2 from 1:

[tex]\[ 1 - 2 = -1 \][/tex]

Therefore,

[tex]\[ g(2) = -1 \][/tex]

3. Combine the results to find [tex]\((f - g)(2)\)[/tex]:

The expression [tex]\((f - g)(2)\)[/tex] is found by subtracting [tex]\(g(2)\)[/tex] from [tex]\(f(2)\)[/tex]:

[tex]\[ (f - g)(2) = f(2) - g(2) \][/tex]

Substitute the values we calculated:

[tex]\[ (f - g)(2) = 13 - (-1) \][/tex]

This simplifies to:

[tex]\[ 13 + 1 = 14 \][/tex]

So, the value of [tex]\((f - g)(2)\)[/tex] is [tex]\(\boxed{14}\)[/tex].